Place the potatoes in a large Dutch-style oven and cover with water.
Bring the pot to a boil and then turn it down to a low boil. Cook the
potatoes, uncovered, for 10-15 minutes, testing them by inserting a
sharp knife through the center of the potato. The potatoes should just
start to yield to the knife. Do not overcook. Drain the potatoes and
place them in a large bowl.

Using a sharp knife, cut the potatoes in halves (if they are small) or
quarters (if they are large). Sprinkle the vinegar over the tops of the
potatoes and then sprinkle them with the chile oil. Toss gently. Add the
dill, shallots, pepper rings, and the salt and pepper. Toss gently. Serve warm.